On the slice spectral sequence

On the slice spectral sequence

We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtra...

On the Grayson Spectral Sequence

One can use next the globalization machinery developed in [S-F] to get a similar looking spectral sequence for any smooth scheme of finite type over a field. Moreover, it’s not hard to see that the resulting spectral sequence coincides with the one constructed in [F-S]. What is nice, however, with this approach is that it avoids completely the use of the paper of Bloch and Lichtenbaum [B-L], wh...

The Slice Spectral Sequence of Mackey Functors for the C4 Analog of Real K-theory

The purpose of this paper is to describe the slice spectral sequence of a 32-periodic C4-spectrum KH (to be defined below in §6, specifically Definition 6.3) related to the C4 norm (defined in [HHRa, §2.2.3]) MU ((C4)) = N4 C2MUR of the real cobordism spectrum MUR. Part of this spectral sequence is illustrated in an unpublished poster produced in late 2008 and shown in Figure 1. It shows the sp...

Spectral sequence compensation based on continuity of spectral sequence

Humans have an excellent ability to select a particular sound source from a noisy environment, called the \Cocktail-Party E ect" and to compensate for physically missing sound, called the \Illusion of Continuity." This paper proposes a spectral peak tracker as a model of the illusion of continuity (or phonemic restoration) and a spectral sequence prediction method using a spectral peak tracker....

THE SLICE SPECTRAL SEQUENCE FOR RO(Cpn)-GRADED SUSPENSIONS OF HZ I